1. 4 OUT OF 3 PEOPLE
STRUGGLE WITH MATH
Tackle the Math
All Things Fractions
2. Fractions
■ A fraction is defined as a part of a whole (e.g.
2
3
)
■ Fraction terms:
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑚𝑜𝑛𝑖𝑛𝑎𝑡𝑜𝑟
■ If the Numerator > Denominator, then the fraction is called improper.
– We can represent improper fractions as mixed numbers.
– E.g.
8
3
can be written as 2
2
3
■ Mixed numbers look like: 𝑤ℎ𝑜𝑙𝑒
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
3. Example 1
Write as a mixed number:
24
7
24
7
→ 7|24
3
−21
3
whole
denominator
numerator
3
3
7
4. Simplifying Fractions
■ We can simplify fractions by multiplying or dividing the numerator and
denominator by the same number.
■ The goal is to reduce fractions to the lowest terms.
■ E.g. Simplify
20
36
– What goes into both 20 and 36?
■
20
36
÷ 4
÷ 4
=
5
9
■ Anything else?
5. Multiplying Fractions
■ Let a, b, c, and d be nonzero integers. Then,
𝑎
𝑐
×
𝑏
𝑑
=
𝑎 × 𝑏
𝑐 × 𝑑
■ We multiply the numerators together then multiply the denominators together.
■ We should always simplify fractions.
■ E.g. Simplify
5
14
×
7
10
■ →
35
140
Which numbers go into both 35 and 140?
■ →
1
4
6. Dividing Fractions
■ Let a, b, c, and d be nonzero integers. Then,
𝑎
𝑐
÷
𝑏
𝑑
=
𝑎
𝑐
×
𝑑
𝑏
=
𝑎 × 𝑑
𝑐 × 𝑏
■ Dividing fractions stinks! Multiplication is much easier.
■ To turn this into a multiplication problem, KEEP CHANGE FLIP
– SAME CHANGE FLIP
■ E.g. Simplify
1
2
÷
2
5
and write the final answer as a mixed number.
■ →
1
2
×
5
2
■ →
5
4
■ → 1
1
4
7. Adding and Subtracting Fractions
■ In order to add or subtract fractions, we need common denominators.
– Multiply each fraction by the other denominator (may require simplifying).
– Find the least common multiple (LCM), then multiply to get LCM.
■ Let a, b, c, and d be nonzero integers. Then,
𝑎
𝑐
±
𝑏
𝑑
=
𝑎 × 𝑑
𝑐 × 𝑑
±
𝑏 × 𝑐
𝑑 × 𝑐
=
𝑎 × 𝑑 ± 𝑏 × 𝑐
𝑐 × 𝑑
■ Let’s look at some examples.
8. Examples
Simplify the following expressions:
2
3
+
1
5
5
6
−
2
3
2 × 5
3 × 5
+
1 × 3
5 × 3
Multiply by other denominator Multiply by other denominator
10
15
+
3
15
→
13
15
5 × 3
6 × 3
−
2 × 6
3 × 6
15
18
−
12
18
→
3
18
We can simplify this further!
3
18
÷ 3
÷ 3
→
1
6
9. Your Turn
Simplify the following expressions:
10
13
×
2
20
7
5
÷
12
15
5
6
+
4
12
11
18
−
1
2
10. UPCOMING
EVENTS
■ Tackle the Math Series
– Why Does Order Matter?
– 4 Out of 3 People Struggle
with Math
– Probably Probability
– Do You Know the Line?
– Beating the System (of
Equations)
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