Key Concepts
- Renaming improper fractions and mixed numbers.
- Fraction of a set.
- Line plots with fractions.
- Mixed numbers.
Renaming Improper Fractions as Mixed numbers
Use multiplication and division to rename improper fractions as mixed numbers
Fraction Bar: The line that separates the numerator and the denominator in a fraction.
![Improper Fractions](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5592.png)
Division Rule: Divide the numerator by the denominator.
E.g.: 4 ÷ 2 = 2
This is the division rule.
Multiplication Rule: Multiplication is an operation used in math to multiply different types of numbers.
Multiplication formula is:
Multiplier × Multiplicand = Product
E.g.:
![7x5=35](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5593.png)
Example: Rename as a mixed number
Sol: = 5 fourths
= 4 fourth + 1 fourth
=
=
=
Example: Rename as a mixed number
Sol:
![6/5](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5591.png)
Renaming Whole Numbers When Adding and Subtracting Fractions
6.6.1 Add fractions to get a mixed number
Example: Add and
to get a mixed number.
![sol](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/sol.png)
6.6.2 Subtract fractions from whole numbers.
Steps:
- Convert the whole number to a fraction.
- Convert to fractions of like denominators.
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/ex.png)
![Subtract fractions from whole numbers.](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5618.png)
6.7 Fraction of a Set
Find a fractional part of a number:
The fractional part of a set is a fraction of the set.
EG: What is of 72?
Sol:
![Find a fractional part of a number:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5621.png)
So, of 72 is 24
6.7.2 Multiply a fraction and a whole number.
We know that multiplication is repeated addition. So, multiplying a fraction by a whole number is equivalent to adding the fraction for the whole number of times.
Example: (a)
Sol: can be shown as:
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5625-1024x216.png)
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7086.png)
(b)
Sol: 5×2 / 3=10 / 3
Real World Problems: Fractions
Example: One-half of the students in a school are girls. of these girls are studying in lower classes. What fraction of girls are studying in lower classes?
Sol: Fraction of girls studying in school =
Fraction of girls studying in lower classes = of
=3 / 5× 1 / 2
=3×1 / 5×1 / 2
=
of girls are studying in lower classes.
Line Plots with Fractions of a unit
Line Plots: A line plot is a way to display data along a number line. Line plots are also called dot plots.
Example: Marcia class measured the snowfall for 5 days. The line plot shows the height of the snowfall they recorded. How many inches of snow were recorded? What amount of snowfall occurred most often?
![Line Plots with Fractions of a unit](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5635.png)
Find the total number of inches of snowfall recorded.
Sol: 1 / 4+2 / 4+2 / 4+2 / 4+3 / 4 = 10 / 4 = 224 inches
Exercise:
- Rename 6/5 as a mixed number.
- Add 8/4 to 1/2 get mixed number
- Find 7- 1/2
- What is 2/4 of 56?
- Find . 9 x 10/3
- Jack measured her dolls and showed the heights using a line plot. What was the most common height?
Height of Jack’s Dolls
![Height of Jack’s Dolls](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5637.png)
- Two friends want to share 3 apples so that they each get same amount. How much would each friend get?
- Two children are sharing 1/2 of a sandwich. How much will each child get?
What have we learnt:
- To change improper fractions to mixed numbers.
- To change mixed numbers to improper fractions.
- Representing a fraction as part of a whole or part of a set.
- To show fractions with line plots.
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