Working with Fractions

1Multiplication of Fractions

To multiply fractions, multiply numerators and multiply denominators: (2/3)×(4/5)=8/15. Of means ×: 2/3 of 12 is (2/3)×12.

Adding numerators while multiplying is a mixed rule.

Figure. Split the whole into 2 rows and 3 columns. One cell is one-sixth — that is 1/2 of 1/3.

How it works

1. Write both fractionsThe given.
2. Multiply tops; multiply bottomsThe product.
3. Simplify if a common factor is obvious8/12 = 2/3.

2Division of Fractions

To divide by a fraction, multiply by its reciprocal: (2/3)÷(4/5)=(2/3)×(5/4). Dividing by 4/5 asks how many 4/5 fit.

Flipping both fractions is a miss — flip the divisor only.

Figure. How many one-fourths sit in three-fourths? Three. Division asks that count.

How it works

1. Keep the first fractionThe dividend.
2. Flip the secondReciprocal.
3. Then multiplyThe quotient.

3Some Problems Involving Fractions

A word problem is a fraction job once you name × or ÷: share 3/4 of a tape, or how many 1/8 cups in 3/4. Write the expression, then compute.

A story without × or ÷ is not yet a problem you can finish.

How it works

1. Name the jobOf, or how many fit.
2. Write × or ÷ of the two fractions (or a whole)The expression.
3. ComputeThe answer with a unit if there is one.

4A definition is a test you can run

A fraction is a parts-of-a-whole (or a division) you can write as a/b with b ≠ 0. The definition-test is: name the whole and the parts.

A slash between two pretty numbers is not a fraction until the whole is named.

How it works

1. Name the wholeOne tape, or 1.
2. Name how many equal parts, and how many you takeb and a.
3. Write a/bThe test passed.

5Name the given before the unknown

The given is the two fractions (or a fraction and a whole). The unknown is the product, quotient, or the of-amount. Write them before you flip anything.

Flipping the first fraction because “division feels like flip” is a silent swap.

How it works

1. Write both given numbersThe given.
2. Name ×, ÷, or ofThe unknown’s job.
3. Then computeGiven first.

6One worked case is enough at this class

One product or one quotient is enough. A worksheet of clones of (2/3)×(4/5) does not add a new rule.

Ten twins still multiply tops and bottoms.

How it works

1. Do one × or one ÷The case.
2. A second only as a checkChange a number.
3. StopThis class.

7A miss: swapping the school name for the picture

A pizza drawing is a setting. The maths is 2/3 × 1/2, not counting pepperoni. Swapping the drawing for the rule is the miss.

Eight slices drawn do not replace the multiply-tops rule.

How it works

1. Keep the pizza as a storyA setting.
2. Write the fraction jobThe maths.
3. Compute the writingDo not swap.

8Check by the opposite action or the opposite test

Check × by asking if the product is smaller when both fractions are proper (less than 1). Check ÷ by multiplying back: quotient × divisor should return the dividend.

Staring at 8/15 and saying “looks small” is not the opposite test.

How it works

1. Get a candidate8/15, or 5/6.
2. Use the size-sense or multiply backThe check.
3. If it fails, mend the flip or the topsHonest.