- Merry Havens

# Solving Word Problems 2

Updated: Aug 19, 2020

Deciphering the meaning of word problems is a useful skill. It takes some practice, like anything new, but it's not hard.

For example:

Delaney has 3 friends she was to share her candy with. She has 32 pieces of candy, how many will she give each friend and herself to share evenly?

Circle our numbers 3 and 32 and underline how many will she give each friend and herself, to remind us of what we need to keep in mind.

First, since she is sharing with her friends, not giving it to them, we have to add 1 to 3 to count herself in.

Second, since she is sharing, we know we will have to divide the number of candies (32) by 4.

Now we are ready to write the equation: 32 / 4

So, Delaney will give each friend 8 pieces and keep 8 pieces for herself.

Basic Word Problem Deciphers

Look for "key" words.

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Certain words mean certain operations. Below is a partial list.

**Use Addition when you see:**

**increased by** eg. 7 increased by 7—> 7 + 7

**more than** eg. 10 more than 29 —> 29 + 10

**combined, together** eg. 12 combined with x —> 12 + x

**total of** eg. A total of 16, 28 and 29 —-> 16 + 28 + 29

**sum, plus** eg. A sum of 15 and 27 —->. 15 + 27

**added to ** eg. x added to 19 ——> x + 19

**Use Subtraction when you see:**

**decreased by** eg. 17 decreased by 12 —> 17- 12

**minus, less** eg. 17 less than 22 —> 22- 17

**difference between** eg. difference between 22 and 7—> 22-7

**less than, fewer than** eg. 17 fewer than 80—> 80 - 17

**take from** eg. take 23 from 45—-> 45 - 23

**Use Multiplication when you see:**

**by** eg. area: a room 14 by 25 —> 14 x 25

**times, multiplied b**y eg. 4 times more than 7—> 4 x 7

**product of** eg. A product of 3 and 4b —> 3 x 4b—> 12b

**increased by a factor** eg. A is increased by a factor of 3->3A

**twice means times 2** eg. Twice the sum of 2 and 3—> 2 x 5

**each** eg. 12 girls each got 25 beads—> 12 x 25

**Use Division when you see:**

**Decreased by a factor** eg. A is decreased by a factor of 3 —>A/3

**per, a** eg. 6 times per 2 weeks—> 6/2 means 3 times a week

**Note** per can be confusing until you understand it’s use in dimensional analysis. Basic example Amy ran 12 miles per week for 15 weeks.

12 miles/week (that’s division) times 15 weeks (multiplication)

It looks like this:

__12 miles__ x 15 weeks = 180 miles

1 week

Multiply numerator numbers together (12 x 15) and denominator numbers (in this case, there is just 1) to get 180, keep the miles units, weeks units in numerator and denominator cancel

**every** eg. 9 apples for every 3 kids—> 9 / 3 means 3 per kid

**out of** eg. 7 out of 21 were boys—> 7 / 21 (meaning 1 out of every 3 were boys, one-third)

**ratio of, quotient of** eg. Ratio of 7 to 10—>7:10 or 7 / 10

**percent** (divide by 100) eg. 25 percent —> 25/100 = .25

**equal pieces, split ** eg. 28 split among 4 boys—> 28 / 4

**average** eg. add each value then divide by the number of values: Average of 12, 16 and 20 —>(12+16+20)/3

**Equals**

**is, are, was, were, will be..... 7 is 3 more than 4. ..... 7 = 3 + 4**

**gives, yields**

**sold for, cost**

Here’s a little word problem to give you some practice with some of these terms:

Sarah has **7 less than 4 times** as many games as Chloe. **Chloe has 100 games**, __how many does Sarah have?__

S(# of Sarah’s games) = 4 times C(# of Chloe’s games) minus 7

**Step 1**, set up equations with variables

S = 4 x C - 7 C = 100

**Step 2**, replace the C in the first equation with 100

S = 4 x 100 - 7

**Step 3**, solve the equation to get S (# of games Sarah has)

S = 400 - 7

S = 393

Sarah has 393 games (7 less than 4 times Chloe’s)

Notice, PEMDAS reminds us to multiply 4 and 100 before we subtract 7. More on PEMDAS and GEMS on a future blog.