“By one more than the one before”
Remembering this sutra when squaring numbers ending in 5 can help you come up with the answer quickly, and without having to write anything down.
For instance: let’s take the number 352. To find the answer the usual way, we’d multiply 35 by 35 by writing down the numbers, doing the multiplication and addition, and finally arriving at 1225. Using this first sutra, “By one more than the one before,” we can do this problem in our heads. The answer has two parts to it: since the number we’re squaring ends in 5, the last two numbers will always be 25, because 5 × 5 is 25. To arrive at the first two numbers, we use the sutra multiplying “by one more than the one before.” In “35,” the number “before” the last number is 3. “One more” than 3 is 4. So we multiply 3 by 4 to get 12. We know the last two digits of our answer will be 25. So 1225 is our answer.
Let’s try another example: 152
We know the last part of our answer will be 25. Following the “by one more than the one before” rule, we need to multiply the first numeral in “15” by one more than itself. So that’s 1 (our first numeral) multiplied by 2 (one more than our first numeral, 1), which equals 2. So our answer is 225.
Another example: 1052
We know the last part of our answer will be 25. Following the “by one more than the one before” rule, we need to multiply 10 by 11 (one more than 10), which equals 110. So our answer is 11025.
“All from 9 and the last from 10”
This is an easy rule for subtracting numbers from 100, 1000, 10000, etc.
In the equation “10,000 - 6347,” you can figure the answer by using “all from the 9 and the last from 10”: subtracting each of the digits in 6347 from 9, except the last digit, which you subtract from 10. So that’s 9 minus 6 (which is 3), 9 minus 3 (which is 6), 9 minus 4 (which is 5), and 10 minus 7 (which is 3), which gives you the answer 3653. This rule works when you have one zero for each digit you’re subtracting—no more, no less. Here are some examples in action:
“Vertically and crosswise”
This can be used for multiplying numbers, and also adding and subtracting fractions. Let’s tackle fractions first, adding 6/7/6/7 and 5/3/5/3. The way we have traditionally been taught to compute this can get a bit complicated. But using “vertically and crosswise,” we can do this in our heads.
To get the “top” part of our answer, we multiply 6 by 3 and 7 by 5. That gives us 18 and 35. Add those together to get our final top number, 53. For the bottom number we multiply the two bottom numbers of our equation, 7 and 3. That gives 21, and so our answer is 53/21/53/21.
Let’s try another example: 3/2/3/2 + 5/6/5/6
To get the top number of our answer, multiply 3 × 6 (that gives us 18) and 2 × 5 (that gives us 10), then add those together (28). To get the bottom number, multiply the two bottom numbers of the equation, 2 and 6. That gives us 12. So our answer is 28/12/28/12.
This works the same with subtracting fractions. Let’s use our second example, subtracting instead of adding this time: 3/2/3/2 - 5/6/5/6
To get the top number of our answer, multiply 3 × 6 (that makes 18) and 2 × 5 (that’s 10), then subtract instead of add: 18 - 10 = 8. That’s our top number. Multiply the bottom two numbers of the equation, 2 × 6, and that gives us our bottom number, 12. Our answer is 8/12/8/12 (which can be further reduced to 2/3/2/3).
“Vertically and crosswise” also works with multiplying numbers. If you’ve memorized your timestables, you might know some basic multiplication by rote. But Vedic math offers a creative way to arrive at answers to long multiplication problems that makes multiplying even more fun.
Multiplying 21 × 23 the usual way will get us an answer of 483, but using Vedic math will help us get there faster. Imagine 23 sitting just below 21 and multiply vertically and crosswise, using the following three steps, to arrive at the answer:
Multiply vertically on the right to get the final digit of the answer: In this case, that’s 1 × 3, which equals 3.
Multiply crosswise and then add to get the middle digit of the answer: In this case, that’s 2 × 3 added to 1 × 2, which gives us 8. (If multiplying crosswise and adding gives you 10 or over, you’ll have to carry over the first digit of the number and add that to the answer in step 3.)
Multiply vertically on the left (and then add any carried-over number, if necessary) to get the first digit of the answer: In this case, that’s 2 × 2, which equals 4.
Here’s another example: 61 × 31
Multiply vertically on the right (1 x 1) to get the final digit of the answer (1); multiply crosswise (6 × 1 and 1 × 3) and then add to get the middle digit (9); and multiply vertically on the left (6 × 3) to get the first digit of your answer (18). The result is 1891.
With two-digit numbers that are close to 100, you can use “vertically and crosswise” as follows. Let’s try 88 x 97. Write out the equation, and then subtract both 88 and 97 from 100, writing the results to the right, as shown on the next page. (100 - 88 is 12, and 100 - 97 is 3, so write 12 to the right of 88 and 3 to the right of 97.)
Now use “vertically and crosswise”: Multiply the two numbers on the right to get the last two digits of your answer—in this case 36 (12 x 3 = 36). Subtract crosswise, either 88 - 3 or 97 - 12 (it doesn’t matter which one you use, as they will both result in the same answer!), to arrive at the first two digits of your answer: 85. So your final answer is 8536.
In some instances, you may have to carry over. For example, let’s try 90 x 76. Write this out as before, with 90 above 76. You can use the “all from 9 and the last from 10” rule to subtract both 90 and 76 from 100: write the corresponding answers to the right, as shown below.
Multiply the numbers on the right to get the last two digits of the answer. But in this case, 10 x 24 gives us 240—a three-digit number. The 2 in 240 is our extra digit, and it must be carried over. Write down 40 beneath the 10 and 24, and carry the 2 over, writing it on top of the 90 so you don’t forget to add it later. Now subtract crosswise, 76 - 10 or 90 - 24. Either way will give you the answer of 66. To that, add the 2 you carried over. That gives you 68, the first two digits of your answer. Your final answer is 6840.
Words to Impress
STRUNK AND WHITE, in The Elements of Style, tell us about sesquepedalian words: “Do not be tempted by a twenty-dollar word when there is a ten-center handy, ready and able.” But daring girls are never afraid to drop a spectacular multisyllabic bombshell when necessary. Here are some you can use when quotidian vocabulary fails.
aleatoric
(EY-lee-uh-tohr-ik) dependent on luck or a random outcome, like a roll of the dice
Aurora just laughed when doubters attributed her triumph over the pirate rogues to aleatoric influences.
brobdingnagian
(brob-ding-NAG-ee-uhn) gigantic, enormous, tremendous
Lydia made constant use of her brobdingnagian vocabulary.
callipygian
(kal-uh-PIJ-ee-uhn) having shapely buttocks
Jen’s callipygian beauty was matched only by her strong right hook.
crepuscular
(kri-PUHS-kyuh-ler) dim; resembling or having to do with twilight
Janet’s habit of planning all her best pranks to occur immediately after dinner led her mother to declare her utterly crepuscular in nature.
diaphanous
(dahy-AF-uh-nuhs) almost entirely transparent or translucent
Halloween had been a success, thought Belinda, even though little kids kept bumping into her costume’s diaphanous fairy wings.
echolalia
(ek-oh-LEY-lee-uh) repeating or echoing a person’s speech, often in a pathological way
The baby’s curious echolalia almost sounded like real conversation.
frangible
(FRAN-juh-bull) fragile; easily broken; brittle
After seeing what happened to his brothers, the third little pig resolved to build his house from a less frangible material.
frustraneou
s
(fruhs-TREY-nee-uhs) vain; useless; frustrating
After several frustraneous attempts, Katie gave up on trying to get her sister’s attention.
gustatory
(GUHS-tuh-tohr-ee) of or pertaining to taste or tasting
Rachael dug into her dinner with gustatory glee.
hagiology
(hag-ee-OL-uh-jee) literature dealing with the lives of saints; a list of saints
Julie’s notebook was practically a hagiology of current boy bands.
ineluctable
(in-ih-LUCK-tuh-bull) inevitable, inescapable (From the Latin word luctari, “to wrestle.”)
Sarah was unable to escape the ineluctable gaze of her mother.
jejune
(ji-JOON) immature, uninteresting, dull; lacking nutrition
Molly resolved to use an interesting vocabulary, the better to avoid appearing jejune.
knurl
(n×rl)
a knob, knot, or other small protuberance; one of a series of small ridges or grooves on the surface or edge of a metal object, such as a thumbscrew, to aid in gripping
Samira learned to rock climb by grabbing onto the knurls all the way up the wall.
languorous
(LANG-ger-uhs) lacking spirit or liveliness; dreamy; lazy
Amelia spent a languorous day by the pool.
luculent
(LOO-kyoo-luhnt) easily understood; clear or lucid
Sometimes Brianna’s homework needed to be a little more luculent.
mellifluous
(muh-LIF-loo-uhs) flowing with sweetness or honey; smooth and sweet
Anna always enjoyed chorus; she knew her voice was mellifluous.
miasma
(mahy-AZ-muh) foul vapors emitted from rotting matter; unwholesome air or atmosphere
Emi held her nose as she passed the miasma of what her little brother referred to as “the stinky parking garage.”
natalitious
(nay-tuh-LIH-shis) pertaining to one’s birthday
Mary designed elaborate invitations to announce her natalitious festivities.
nemesis
(NEM-uh-sis) a source of harm; an opponent that cannot be beaten; mythological Greek goddess of vengeance
On a good day, Christina’s brother was her ally; on a bad day, he was her nemesis.
obsequious
(uhb-SEE-kwee-uhs) fawning; attentive in an ingratiating manner
Eager to win her parents’ approval, Vanessa was polite to the point of being obsequious.
persiflage
(PURR-suh-flahzh) light banter; frivolous discussion
“We must be careful to keep our persiflage to a minimum,” Nola whispered to Margot during class.
quiescence
(kwee-ES-uhns) stillness, quietness, inactivity
Esme reveled in the extraordinary quiescence of early morning when she awoke before anyone else.
quotidian
(kwoh-TIHD-ee-uhn) everyday, commonplace, ordinary; recurring daily
Dana sighed, bored by the quotidian sameness of it all.
rapprochement
(rap-rohsh-MAHN) reconciliation; the reestablishing of cordial relations
After holding a grudge against him for so long, Eleanor felt it was almost a relief to have reached a rapprochement with her brother.
risible
(RIZ-uh-buhl) laughable, causing laughter
The girls knew they could always count on Jasmine for a risible remark.
sesquipedalian
(SESS-kwih-puh-DAY-lee-un) characteristic of a long word; given to using long words
Daring girls are not shy about their sesquipedalian abilities.
sprezzatura
(SPRETTS-ah-TOO-ruh) nonchalance, effortlessness
After reading The Daring Book For Girls, Erin was able to cartwheel with sprezzatura and verve.
Truculent
(TRUCK-yuh-lunt) pugnacious, belligerent, scathing
When Nancy was pushed too far, she became truculent.
ultracrepidarian
(ull-truh-krep-ih-DAIR-ee-uhn)
giving opinions or criticizing beyond one’s own range of expertise
“I’d tell you what I think about your outfit, but I don’t want to be all ultracrepidarian,” said Karen.
vitiate
(VISH-ee-ayt) to weaken, impair, or render invalid
Penelope’s debate in class vitiated Rob’s argument.
winsome
(WIN-suhm) sweetly or innocently charming
Surya was too busy building her tree fort to act winsome.
xenophobe
(ZEE-nuh-fohb) a person who fears or hates foreigners
It was a nerve-racking moment at the potluck picnic, when the neighborhood xenophobe showed up with potato salad.
yawl
(Yawl) a ship’s small boat; a yowl or howl
Lanie let out a loud yawl as the boat tipped over.
zaftig
(ZAHF-tik) having a shapely figure (From the Yiddish word zaftik, “juicy.”)
Beyonce was proud of her strong, zaftig figure.
zeitgeist
(TSIYT-giyst) the spirit of the time; the outlook of a particular generation
Shonda was convinced the latest pop star embodied the zeitgeist of middle school.
Tree Swing
WHAT YOU NEED
♦ Wood, 2 × 8, 2 ″ long
♦ Rope
♦ Two eyebolts, 8″ long, with a 3/8/3/8″ thread, two nuts and four washers
♦ A tennis ball, a sock, and some twine
♦ Drill with 3/8/3/8″ bit
THE HARDEST PART of building a tree swing is finding a well-suited branch. We can tell you that a tree-swing branch should be at least 8 inches in diameter, but on a tree tall enough for a swing, that can be difficult to measure precisely. You’ll also need a strong rope long enough to get around the branch and down to the ground and back up again.
Your swing should not be on a white birch, because those rubbery branches readily bend. Look for a hardy oak or maple. The spot on the branch where you hang your swing should be far enough from the trunk so no one is hurt when they swing, but close enough so the branch is still strong.
The second hardest part is getting the rope up and over the branch. To forestall several hours of standing with a rope and squinting into the sun, we have a strategy to suggest:
Put a tennis ball in an old sock. Wrap twine around the sock and make a knot so the tennis ball stays put, and make sure you have enough twine on the skein so it can unfurl the length up to the tree branch, and back down again.
Stand under the tree and aim the tennis-ball-in-the-sock over the branch. It may take a few tries, but it is much easier than just flinging the rope up to the branch.
Once up-and-over, the tennis ball sock will land near your feet, trailed by a long strand of twine. Knot the twine to the rope to be used in the tree swing. (Try a sheetbend knot, it’s designed to join different sized-ropes.) Pull the twine until the rope is over the branch. You might want to toss the ball/rope combo over again, to double-loop the rope over the branch. When all is in place, detach the twine. The rope is set.
The easiest part is making the seat and procuring a long length of knot. Find or cut a 2-foot long piece of 2-by-8 wood. Draw a line down the center, lengthwise, and measure 2 inches in from either side. That’s where to drill the two holes. Put an eyebolt through each hole, with a washer above the wood and a washer and nut below it. Knot the two ends of the rope to the eyes of the eyebolt (a tautline hitch is handy here).
If you don’t want to use the bolts, you can push the ropes themselves through the holes and tie with strong stopper knots.
Yoga: Sun Salutation
(surya namaskara)
THE WORD yoga comes from the Sanskrit root yuj, “to yoke,” or “to unite” and dates roughly from 5000 BC according to Vedic texts. In the Sun Salutation, as with all flowing or dynamic yoga postures, what is joined
is your movement and your breathing. The Sun Salutation—surya namaskara in Sanskrit—is done differently depending on which style of yoga you choose to follow, but in its most basic form, it is a series of 12 or so postures (asanas) linking movement with inhalation and exhalation. Here is the Ashtanga yoga version of the most basic sun salutation.
The most important thing to keep in mind when doing any kind of yoga is your breathing: inhaling with each extension or stretch, and exhaling as you fold or contract. The best way to breathe during this exercise is to first suck in your stomach so that it feels like your belly button is pulled back toward your spine. Now keep it there and breathe—through your nose, with your mouth closed—deeply into your chest. Your chest should rise and fall with your breath as your stomach stays tight, and you should breathe this way through the entire series.
Traditionally, the sun salutation is performed at sunrise—if you’re really hard-core, it’s done just before dawn, facing the east, with mantras and libations in honor of the sun god, but you don’t have to go that far. First thing in the morning, on an empty stomach, is ideal enough. In fact, the sun salutation can be done any time you feel like taking a moment to breathe, move, and become energized. It can be a foundation for your yoga practice, or it can be a practice in and of itself. Either way, the sun salutation is something you can do for the rest of your life.
The Daring Book for Girls Page 23
