Unit 5: Common Fractions & Decimals
Topic B: Comparing Fractions & Decimals
In Unit 2 you compared simple fractions to simple fractions such as 1212 1313
Now, you are going to be asked to compare fractions with larger and less common denominators such as 7878 and 17281728
Find the equivalent fractions of both the fractions and then compare.
12(×3×3)=3612(×3×3)=36 and 13(×2×2)=2613(×2×2)=26 so 36≥2636≥26
78(×7×7)=495678(×7×7)=4956 and 1728(×2×2)=34561728(×2×2)=3456 so 4956≥34564956≥3456
Exercise 1
Change the fractions to have the same denominators. Decide which is larger. Use > , < , = to mark your answer. There is space below each problem to work out your equivalent fractions.
- 1414 3535
- 5858 3434
- 1515 2323
- 2323 3434
- 49564956 3434
- 75907590 10111011
- 33703370 1212
- 1313 1919
Answers to Exercise One
- <
- <
- <
- <
- >
- <
- <
- >
Comparing Fractions to Decimals and Decimals to Fractions
Now that you know how to convert between fractions and decimals, you are also going to be able to compare them.
Example A
Which is larger: 3838 or 0.125?
- Decide to convert either the fraction into a decimal, or the decimal into a fraction. Let’s pick converting the fraction into a decimal.
- Do the conversion3838 =0.37583.00024↓ 6056↓4040 = 0.375
- Compare 0.375>_0.125
- Write a math sentence to show your answer: 38>_0.125
Example B
Which is larger78 or 0.6?
- Pick which you will convert, the decimal into the fraction, or the fraction into the decimal. Let’s pick converting the decimal this time.
- Convert 0.6= 610(÷2÷2)=35
- Compare 7835⟶78(×5×5)=354035(×8×8)=2440
- Write a math sentence to show your answer 38>_0.6
TIP: You may find that converting the fractions to the decimals could speed things up.
Exercise 2
Compare
- 0.25 15
- 18 0.8
- 16 0.125
- 0.2 310
- 0.3725 23
- 25 0.5
- 0.3725 15
Answers to Exercise Two
- >
- <
- >
- <
- <
- <
- >
Exercise 3
Compare the following numbers to each other. Use > or < .
- 0.345 67
- 11051 0.0032
- 0.52 23
- 0.6894 103278
- 172 23
Answers to Exercise Three
- >
- <
- >
- <
- <
Topic B Self-Test
Mark /18 Aim 15 / 18
- Write as common fractions in lowest terms. (4 marks)
- 3.6
- 8.125
- 0.75
- 0.45
- Write as decimals. Round your answers to 3 decimal places. (4 marks)
- 35
- 6100
- 38
- 57
- Compare the following fractions and decimals, use < , or >. (6 marks)
- 0.862 67
- 314 0.35
- 110 0.007
- 0.3 2026
- 0.5 1021
- 8990 0.473
- 13 19
- Problems. 4 marks
- May babysat for 414 hours. She is paid $4.75 an hour. How much did she earn?
- Diane bought 1.5 litres of milk. Her thirsty kids drank half of it as soon as she got home. How much milk is left?
Answers to Topic B Self-Test
-
- 31021
- 818
- 34
- 920
-
- 0.3
- 0.06
- 0.375
- 0.174
-
- >
- <
- >
- <
- >
- >
-
- $20.19
- 0.75 L