Math 064 – Day 18
Name: _________________________________
Building Fractions to Higher Terms and Reducing Fractions to Lowest Terms
1. Warm-up:
a. Mathematically, find 4 fractions that are equivalent to:
8
. Show your work
12
b. Use your fraction strips to show that your answers are correct. Were you able to
model all of your answers with your fraction strips?
Remember:
One way to find an equivalent fraction is to multiply the _______________________
and the __________________________ of a fraction by ________________________.
This process is called building the fraction to higher terms.
Notes: Building a Fraction to Higher Terms
2. Together: Let’s find 3 equivalent fractions by building to higher terms. Where possible,
model with fraction strips to check your answers.
5
7
a.
b.
8
12
1
3. With a partner: Find 3 equivalent fractions for each fraction below by building to higher
terms. Where possible, model with fraction strips to check your answers.
3
5
a.
b.
5
6
4. Together: What if we need to find a fraction equivalent to a given fraction, but we already
know what the denominator needs to be? Let’s try these together.
Directions: Find the missing number. Where possible, model with fraction strips to
check your answers.
7
n
5
b.

a.

18 54
8
24
5. With a partner: Find the missing number. Remember, where possible you can model with
fraction strips to check your answers.
4 n
11
b.

a.

5
20
12
24
c. Find a fraction equivalent to
d. Find a equivalent to
3
whose denominator is 35.
7
1
whose denominator is 84.
2
6. Together: Let’s notice something about equivalent fractions. In problem 2a, we saw that:
5 10

Let’s find the cross products: 5 16  _____ and 8 10  ______
8 16
What do you notice about those cross products? _________________________________
Question: If fractions are equivalent, will the cross products always be the same?
5 15
We found that: 
. Find the cross products. 5  24  _____ and 8 15  _____
8 24
Are they the same?
2
7. With a partner:
a. Check your answers for problem 3a by finding cross products and seeing if they are
equal.
b. Check your answers for problem 3b by finding cross products and seeing if they are
equal.
Notes: An important property of equivalent fractions is that their _____________________
are always _____________.
8. Together: Find n and check by finding cross products.
4 n
5
n
a.
b.


9 27
16 80
9. With a partner: Find n and check by finding cross products.
7
n
7 n
a.
b.


12 36
8 56
Remember:
Another way to find an equivalent fraction is to divide the ______________________
and the __________________________ of a fraction by ________________________.
This process is called reducing or simplifying the fraction.
Notes: Reducing (Simplifying) a Fraction to Lowest Terms
3
10. Together: Simplify (Reduce to lowest terms). Check your answer by cross multiplying.
8
16
a.
b.
12
80
c.
54
126
d.
7
24
11. With a partner: Reduce to lowest terms. Check your answers by cross multiplying.
6
18
a.
b.
8
24
c.
32
48
d.
8
36
e.
9
19
f.
24
78
g.
48
80
Homework: pp. 88 – 89: 35 – 57
4