Unit 3: Linear Equations - Multiplying And Dividing Fractions 2 Worksheet With Answer Key Page 6
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How to
• • • • • • • • • • • • • • • • • • • Divide Fractions
Facts to Know
(cont.)
Canceling in Dividing Fractions
Sometimes you can cancel in division. Invert before you cancel and multiply after you cancel.
Sample: 1 –
÷ 1 –
= ?
3
6
Invert and change to multiplication. 1 –
÷ 1 –
= 1 –
x 6 –
Step 1
3
6
3
1
Step 2
3 is a factor of 3 and 6. Cancel and
divide the numerator and denominator by 3. 1 –
x 6 –
3
1
2
Multiply. 1 –
x 6 –
= 2 –
Step 3
= 2
3
1
1
1
Dividing a Fraction by a Whole Number
When dividing a fraction by a whole number, first change the whole number to a fraction with a
denominator of 1.
Sample: Suppose a recipe calls for dividing 1 –
pound of butter into four equal parts.
2
Hint: You must divide 1 –
by 4.
2
Change the whole number, 4, to a fraction. 4 = 4 –
Step 1
1
Invert the divisor. 4 –
inverted is 1 –
Step 2
1
4
Multiply. 1 –
x 1 –
= 1 –
Step 3
pound of butter.
2
4
8
Dividing a Whole Number by a Fraction
Sometimes the whole number is not the number you are dividing by—it is the number being divided.
Sample: Divide 4 pounds of candy into bags holding 1 –
pound each.
2
Hint: You must divide 4 by 1 –
.
2
Change the whole number to a fraction. 4 = 4 –
Step 1
1
Invert the divisor. (Invert the number to the right of the division sign.) 1 –
Step 2
inverted is
2
2 –
1
Multiply. 4 ÷ 1 –
= 4 –
x 2 –
= 8 –
Step 3
or 8 bags
2
1
1
1
Dividing and Mixed Numbers
Before dividing, change any mixed numbers to improper fractions.
Sample: 1 1 –
÷ 2 –
= ?
4
3
Change the mixed number to an improper fraction. 1 1 –
= 5 –
Step 1
4
4
Invert and multiply. 5 –
x 3 –
= 15 —
= 1 7 –
Step 2
4
2
8
8
18
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