Fractions and mixed numbers

Fractions and mixed numbers

The uses in daily life

Fraction basics

A fraction has 2 parts.  A numerator which is the top value and a denominator which is the bottom value.  The numerator is the part of the whole value.  Ex.  1/4 tells me that 1 out of 4 is the part representing this picture.

Each piece of this diagram is 1/4 making the total number of pieces 4/4.

Proper and improper fractions

• Proper fractions- numerator is smaller than the denominator.

• Improper fractions- numerator is equal to to larger than the denominator.

• Improper fractions can be converted into mixed numbers.

Multiple Select

Which represents an improper fraction?

• 2/5

• 5/2

Changing improper to mixed number

• 45/8 can be changed to an mixed number.

• Divide the numerator 45 by the denominator 8.

• Dividing will give a whole number of 5.

• The remainder will now be made into a fraction of 5/8.  This means 5 out of the 8 are left.

• The final answer is 5 5/8.

Converting a mixed number into a improper fraction.

• 3 2/5 can be made into an improper fraction.

• Multiply the denominator 5 by 3 the whole number.  This will give you 15

• Add 15 to the numerator of 2.  This will give you 17.

• The improper fraction will be 17/5.

Equivalent fractions

Two fractions are said to be equivalent if they represent the same value. Ex.  2/3 is the same as 6/9 because both the numerator and the denominator were multiplied by 3.  This makes them equivalent.

Are they all equivlent?

Multiple Select

Check the equivalent fractions that are the same as 2/7.

• 6/21

• 1/7

• 10/35

• 14/28

Reducing fractions

• Opposite of finding equivalent fractions.

• Reducing or simplifying fractions is asking that you find the lowest values in the numerator and the denominator by dividing by the same value.

Multiplying and Dividing Fractions

• When you multiply fractions, multiply the numerators and the denominators. Simplify if you need to in the end.

•  $\frac{3}{4}\times\frac{24}{15}\ =\ \frac{3\ x\ 24}{4\ \times\ 15}\ =\ \frac{72}{60}=\ \frac{6}{5}\ =\ 1\frac{1}{5}$  

• Notice: the improper fraction was simplified before being made back into an mixed number.

Multiple Choice

5/6 x 1/4=

• 5/8
• 1/4
• 5/24
• 1/5

Dividing fractions

• Dividing fractions is similar to multiplying fractions, the difference is the second fraction is flipped or reciprocals are used.

•  $\frac{3}{5}\div\frac{12}{15}=\frac{3}{5}\ x\ \frac{15}{12}\ =\ \frac{45}{60}=\frac{3}{4}$  

• In the example, the second fraction  $\frac{12}{15}$  was the reciprocal.  When the flip takes place the problem then becomes multiplication.  The final answer was simplified by dividing by 15.

Multiple Choice

¹/₄  ÷  ²/₅

• ⁵/₈
• 2/20
• ¹/₁₀
• ³/₉

Whole numbers and multiplying or dividing by fractions.

• When you have a whole number in the problem and you are multiplying or dividing, you can make the whole number into a fraction by putting the whole number over 1.

• Ex: 5 x  $\frac{1}{2}$  =  $\frac{5}{1\ }\ \times\ \frac{1}{2}=\frac{5}{2}=\ 2\ \frac{1}{2}$  

• Division will use the same method but you need to pay attention where the whole number is in the problem.  If it is the second term then this will be the reciprocal term.

Multiple Choice

Divide. 3 ÷ 2/5

• 2/15
• 5/6
• 1  1/5
• 7  1/2

Multiplying and dividing mixed numbers

• When working with mixed numbers, it is easier to convert the mixed number into an improper fraction before solving the problem.

•  $1\ \frac{2}{3\ }\times\ \frac{3}{5}\ \ =\ \frac{5}{3}\ x\ \frac{3}{5}\ =\ \frac{15}{15}=\ 1$  

Review

• The next slides will review what you learned in this lesson.

Multiple Choice

Reduce the following fraction:
75/81

• 25/27
• 4/5
• 26/27
• it cannot be reduced any further

Multiple Choice

Reduce the following fraction:
16/20 =

• 8/10
• 4/5
• 1/2
• 16/20

Multiple Choice

Multiply

• 6
• 4 / 45
• 20
• 7 /45

Multiple Choice

Multiply 2/6 x 3/5

• 1/5
• 1 / 1
• 1 / 6
• 0

Multiple Choice

Write the improper fraction as a mixed number

²²/₃

• 7 ²/₃

• 7 ¹/₃

• 7 ¹/₄

• 7 ³/₄

Multiple Choice

Write the improper fraction as a mixed number

²³/₅

• 4 ³/₅

• 4 ⁵/₃

• 5 ³/₄

• 4 ³/₄

Multiple Choice

Which symbol is correct for these two fractions?

• >

• <

• =

Multiple Choice

Which symbol is correct for these two fractions?

• >

• <

• =

Multiple Choice

What fraction is green?

• 1/4
• 2/4
• 2/3
• 2/3

Multiple Choice

• 3/4

• 3/5

• 1/4

• 3/6