Lesson 18 of 19

Track quiz

10 min

Text size

Fourteen ideas, fourteen checks. The table goes first, so there is somewhere to look back at.

Fourteen moves for fractions, from the first rename to the last fraction of what is left
Move	How it goes
Name an amount past one whole	Count every piece for the top-heavy name. Count filled wholes first for the mixed one.
Swap between the two names	Whole times the bottom, plus the top. Or share the top into bottoms.
Find a shared bottom number	Count up in steps of each bottom number until both lists meet.
Add unlike fractions	Rename both onto the shared bottom number. Add the tops. Keep the bottom.
Subtract unlike fractions	Rename the same way, then take the tops. Never subtract the bottoms.
Combine mixed numbers	Flatten both, or carry and borrow between wholes and parts.
Take a fraction of a whole number	Divide by the bottom, multiply by the top.
Multiply two fractions	Tops together, bottoms together. No shared bottom needed.
Say which way a product moves	Top under bottom shrinks. Top over bottom grows. Equal leaves it.
Divide by a fraction	Count how many copies fit, or multiply by the flip.
Cancel first	Before multiplying, divide a top and a bottom by the same number. The answer stays the same.
Share a fraction	Multiply the bottom number by the number of shares. The top stays.
Which way dividing moves	Dividing by a number between 0 and 1 makes the amount bigger. Dividing by a number above 1 makes it smaller. Dividing by 1 leaves it alone. That holds for any amount above zero.
What is left	Find what is left first. Then take the fraction of that, not of the whole.

You have 7 third-pieces of a paper strip. What is that as a mixed number?

7 1/3
3 1/7
2 1/3

Which bottom number can both 1/2 and 1/5 be renamed onto?

10
7, because 2 + 5 = 7
5, because 5 is the bigger one

What is 1/4 + 1/3?

2/7
7/12
1/12

What is 5/6 − 1/3?

4/3
4/6
3/6, which is 1/2

What is 2 1/3 + 1 5/6?

4 1/6
3 6/9
4 6/9

Two fifths of 20 tiles is how many tiles?

What is 3/5 × 2/3?

5/8
6/8
6/15, which is 2/5

30 is multiplied by each of 4/5, 5/5 and 6/5. Which one comes out bigger than 30?

30 × 6/5
30 × 4/5
30 × 5/5

What is the reciprocal of 7?

7/1, since a whole number already has 1 underneath
1/7
1/1

How many twelfths fit inside 5/6?

1/10
5/72
10

What is 8/15 × 9/10, if you cancel first?

12/25
12
17/25

What is 7/9 ÷ 3?

7/3
3/7
7/27

30 is divided by each of 3/5, 5/5 and 6/5. Which one comes out bigger than 30?

30 ÷ 3/5
30 ÷ 5/5
30 ÷ 6/5

A rope loses 1/3 of its length. Then 1/4 of what is left is cut. What part of the rope remains?

5/12
1/2
1/12

Chapter 8 of Part I is Working with Fractions. You have placed pieces on strips and matched bottom numbers. You have shared a whole into groups. You have seen a multiplier below one shrink an amount.

Next: Geometric Twins. Two figures that match exactly. And the tests that tell you so without measuring everything.

Reveal every answer to finish this lesson.

Checking your sign-in…

Who's learning?

Track quiz