Lesson 1T ~ Simplifying Fractions
Name__________________________________________
Period______
Date____________
Write an equivalent fraction for each given fraction.
×
×
1.
6
10
=
30
5
6
2.
20
=
×
×
Make two of
your own!
÷
3.
3
15
=
5
4.
2
8
=
=
÷
Find the greatest common factor (GCF) of each pair of numbers.
5.
5 and 10
6.
4 and 2
Factors of 5: _____ , _____
Factors of 4: _____ , _____, _____
Factors of 10: _____ , _____, _____, _____
Factors of 2: _____ , _____
GCF = _______
GCF = _______
7.
30 and 40
GCF = _______
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8.
12 and 16
GCF = _______
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Write each fraction in simplest form.
9.
4
12
a. What number divides evenly into the top and bottom of the fraction? ____
÷
b. Divide both numbers by this number.
4
12
÷
c. Check to see if there are any other numbers that you can divide by. If so, repeat parts a
and b until your fraction is in simplest form.
Write each fraction in simplest form.
10.
2
10
11.
10
25
12.
9
15
13.
4
20
Write each fraction in simplest form. Tell whether or not the pair of fractions is equivalent.
14.
10
5
and
30
15
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15.
12
4
and
42
24
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Lesson 2T ~ Mixed Numbers and Improper Fractions
Name__________________________________________
Period______
Date____________
Write the improper fraction and mixed number for each drawing.
1.
2.
Improper Fraction _________
Improper Fraction _________
Mixed Number _________
Mixed Number _________
Write each mixed number as an improper fraction.
3. 2 13
a. Multiply the whole number by the denominator.
2 ∙ 3 = ___
b. Add the numerator to the answer from part a.
___ + 1 =___
c. Write the answer from part b above the original denominator.
3
4. 3 12
5. 2 54
6. 4 15
7. 10 23
8. Yao can long-jump 6 14 feet. Write this distance as an improper fraction.
9. Rachelle cut off 5 34 inches of her hair. Write this amount as an improper fraction.
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Write each improper fraction as a mixed number.
7
10.
4
a. Color in 7 fourths of the circles.
How many full groups of 4 are in 7? _____
b. How many are left over? ____
c. Write
7
as a mixed number.
4
11.
8
3
12.
9
4
13.
22
5
14.
33
10
15. Ginny’s guppy weighed
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19
6
ounces. Write this amount as a mixed number.
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Lesson 3T ~ Adding and Subtracting Fractions
Name__________________________________________
Period______
Date____________
Find the least common multiple (LCM) of the numbers given.
1. 4 and 6
2. 3 and 5
Multiples of 4: 4, 8, ____, ____, ____
Multiples of 3: 3, 6, ____, ____, ____
Multiples of 6: 6, 12, ____, ____, ____
Multiples of 5: 5, 10, ____, ____, ____
LCM = ______
LCM = ______
3. 5 and 2
4. 6 and 10
Multiples of 5: ____, ____, ____, ____, ____
Multiples of 6: ____, ____, ____, ____, ____
Multiples of 2: ____, ____, ____, ____, ____
Multiples of 10: ____, ____, ____, ____, ____
LCM = ______
LCM = ______
Find each sum or difference. Write your answer in simplest form.
5.
1 2
+
5 5
6.
5 2
−
9 9
7.
1 3
+
4 4
8.
3 1
−
5 5
9.
2 1
−
3 3
10.
1 3
+
7 7
11.
3 1
−
8 8
12.
8
2
+
15 15
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Remember to
simplify your
answer.
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TO ADD AND SUBTRACT FRACTIONS WITH UNLIKE DENOMINATORS
1. Find the Least Common Denominator
2. Rewrite the fractions with the LCD
3. Add or subtract
4. Simplify your answer
Find each sum or difference. Write your answer in simplest form.
13.
3 1
+
5 10
a. LCD = _______
3
=
5
b. Rewrite the fractions with the LCD
c. Add the new fractions
+
1
=
10
=
14.
4 1
−
7 2
15.
2 1
+
3 6
16.
4 1
+
9 6
17.
7 5
−
8 6
18. Michelle rode her bike 34 of a mile on Tuesday and 15 of a mile on Wednesday. What was the
total distance she rode her bike for the two days combined?
©2008 SMC Curriculum
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Lesson 4T ~ Multiplying and Dividing Fractions
Name__________________________________________
Period______
Date____________
Find each product. Write your answer in simplest form.
1.
1 1
⋅
2 3
3.
1 3
⋅
2 4
5.
3 1
⋅
5 4
1 ⋅1 =
2⋅3 =
=
2.
2 1
⋅
3 4
4.
2 4
⋅
5 7
6.
3 5
⋅
4 6
2 ⋅1 =
3⋅ 4 =
=
=
Remember
to simplify
your answer
if needed.
7. Caroline has 13 gallon of paint. She wants to use half the paint to paint her bike. How much
paint will she use?
Find each quotient. Write your answer in simplest form.
8.
1 1
÷
5 3
1 3
⋅
5 1
1⋅ 3 =
5 ⋅1 =
Rewrite as a × problem
with the reciprocal of
the second fraction.
9.
3 1
÷
4 4
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⋅
Oregon Focus on Rational Numbers & Equations
Find each quotient. Write your answer in simplest form.
10.
3 2
÷
7 5
11.
3 1
÷
4 2
12.
1 1
÷
6 3
13.
5 2
÷
6 3
14. Haley has 34 yard of fabric. The belts she wants to make for her friends each take
fabric. How many belts can Haley make?
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1
8
yard of
Oregon Focus on Rational Numbers & Equations
Lesson 5T ~ Operations with Mixed Numbers
Name__________________________________________
Period______
Date____________
Find each sum or difference. Write your answer in simplest form.
1.
2 12 + 3 14
a. Rename each mixed number as an improper fraction: 2 12 =
b. Are the denominators different? ______
If so, rename each fraction using the LCD.
3 14 =
+
c. Add the numerators of the fractions from part b.
+
=
d. Write the sum over the common denominator.
e. Simplify your answer.
2 12 + 3 14
2.
3 14 + 1 13
4. 4 13 + 1 56
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= _______
3. 2 34 − 1 13
5. 2 54 − 1 12
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Find each product or quotient. Write your answer in simplest form.
6.
(3 12 )(2 23 )
a. Rename each mixed number as an improper fraction.
3 12 =
2 23 =
b. Multiply across the top and the bottom of the fraction.
c. Simplify your answer.
(3 12 )(2 23 )
7. 3( 4 14 )
9. 3 12 ÷ 78
= _______
8.
Remember to use
the reciprocal for
division problems.
(1 13 )(2 23 )
10. 4 12 ÷ 3 23
11. Amos bought 2 14 pounds of nails and 3 18 pounds of bolts. How many total pounds of supplies
did Amos buy?
©2008 SMC Curriculum
Oregon Focus on Rational Numbers & Equations
Lesson 6T ~ Adding and Subtracting Decimals
Name__________________________________________
Period______
Date____________
Find each sum or difference.
1.
5.4
+1.8
2.
6.2
−5.1
Rewrite decimal
problems vertically.
3. 4.8 + 1.1
4. 11.8 − 6.2
5. 6.5 + 2.7
6. 4 − 1.8
7. 7.3 − 2.9
8. 15.4 + 8.8
9. 8.51 − 2.17
10. 1.6 + 0.05
Rewrite vertically
with the decimals
lined up.
11. Henry filled his car with gas for $40.55. The next week he filled his car again and the
cost was $45.28. How much did Henry spend on gas in all?
©2008 SMC Curriculum
Oregon Focus on Rational Numbers & Equations
Lesson 7T ~ Multiplying and Dividing Decimals
Name__________________________________________
Period______
Date____________
Find each product.
2.
2.2
× 0.4
3. 4.3
× 6
4.
5.4
× 2.6
5. 3 (1.5)
6. 2.3(0.8)
1.
1.3
× 5
Because there is one
number to the right
of the decimal, move
your decimal in one
space in the answer.
Be sure to move
the decimal twice
in this problem.
7. Munson’s cell phone company charges him $0.12 per minute if he goes over his pre-purchased
minutes for the month. Last month he went over by 8 minutes. How much extra did he owe on
his bill?
8. Sammie wanted to make a ring out of silver. At the jeweler, silver cost $9.55 per ounce. Sammie
bought 3 ounces. How much did she spend?
©2008 SMC Curriculum
Oregon Focus on Rational Numbers & Equations
DIVIDING WITH DECIMALS
1. Make the divisor a whole number by moving the decimal point to the right
2. Move the decimal point in the dividend the same number of spaces
3. Move the decimal point up into the answer
Find each quotient.
9.
0. 3 3.9
∙
11. 1.1 0.88
13.
0.4 4.8
10. 0.4 1.64
12. 0.5 0.065
14. 1.2 36
15. Mickey had $2.55 in bottle returns. If each bottle was worth $0.05, how many bottles did
Mickey recycle?
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Oregon Focus on Rational Numbers & Equations