Checking Reasonableness of Fraction Sums II
You may have learned about using benchmarks to estimate the value of fractions.
Now watch this video to learn how to estimate calculations for addition and subtraction of fractions.
When plotting fractions on a number line we use:
- the denominator to divide the whole numbers into equal parts
- the numerator to select the number of parts.
Knowing approximately how close they are to other known fractions is important for understanding the value of fractions and helps us make sure our answers are reasonable.
The denominator tells us how many parts make the whole.
The numerator tells us how many parts in the fraction.
Knowing how the number line is divided up helps us to understand the value of fractions.
Examples
Question 1
Hermione is working on a problem and has to calculate $\frac{1}{24}+\frac{8}{33}$124+833. She says the answer is about $\frac{1}{4}$14. Let’s see if her estimate is reasonable.
Let’s look at $\frac{1}{24}$124. Which value below is the best estimate of $\frac{1}{24}$124?
$0$0
A$\frac{1}{2}$12
B$2$2
C$1$1
DNow let’s look at $\frac{8}{33}$833. Which value below is the best estimate of $\frac{8}{33}$833?
$4$4
A$\frac{1}{4}$14
B$0$0
C$1$1
DWe can rewrite the fraction sum using the rounded values.
Calculate the fraction sum $0+\frac{1}{4}$0+14.
Is Hermione's estimate reasonable?
No
AYes
B
Question 2
Tracy is working on a problem and has to calculate $\frac{14}{15}+\frac{48}{65}$1415+4865. She says the answer is about $\frac{7}{4}$74. Let’s see if her estimate is reasonable.
Let’s look at $\frac{14}{15}$1415. Which value below is the best estimate of $\frac{14}{15}$1415?
$1$1
A$0$0
B$2$2
C$\frac{1}{2}$12
DNow let’s look at $\frac{48}{65}$4865. Which value below is the best estimate of $\frac{48}{65}$4865?
$0$0
A$1$1
B$\frac{3}{4}$34
C$3$3
DRewrite the fraction sum using the rounded values. Do not add the values together.
Calculate the fraction sum $1+\frac{3}{4}$1+34.
Is Tracy's estimate reasonable?
No
AYes
B
Question 3
Irene is working on a problem and has to calculate $\frac{33}{45}-\frac{6}{25}$3345−625. She says the answer is about $\frac{1}{2}$12. Let’s see if her estimate is reasonable.
Let’s look at $\frac{33}{45}$3345. Which value below is the best estimate of $\frac{33}{45}$3345?
$\frac{3}{4}$34
A$1$1
B$0$0
C$3$3
DNow let’s look at $\frac{6}{25}$625. Which value below is the best estimate of $\frac{6}{25}$625?
$4$4
A$\frac{1}{4}$14
B$1$1
C$0$0
DRewrite the fraction difference using the rounded values. Do not evaluate the subtraction.
Calculate the fraction difference $\frac{3}{4}-\frac{1}{4}$34−14.
Is Irene's estimate reasonable?
No
AYes
B