Hard Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write 0.375 as a fraction in simplest form.

Correct! 0.375 = 3751000 = 38 in simplest form.

(2) Write the reciprocal of 117.

Perfect! Reciprocal means flip the fraction.

(3) Multiply 0.25 by 0.125.

Excellent! 0.25 × 0.125 = 0.03125.

(4) Write 4 35 as an improper fraction.

Great! 4×5+35 = 235.

(5) Convert 278 into a mixed fraction.

Short Answer Questions (2 Marks Each)

Answer each question with proper working

(1) Add 712 and 518.

Perfect! Cannot be simplified further.

(2) Subtract 1315 from 1920.

Excellent! Simplified to 1/12.

(3) Multiply 56 by 910.

Correct! Simplified by dividing by 15.

(4) Divide 0.72 by 0.9.

Perfect! Multiply both by 10 to remove decimals.

(5) A jug contains 3.5 litres of milk. If 1.75 litres is used, how much milk is left? litres

Excellent! 1.75 litres of milk is left.

Long Answer Questions (4 Marks Each)

Note: Answer each question with complete working and clear explanations.

(1) A basket has 12.5 kg of mangoes and 9.75 kg of bananas. Find the total weight of fruits in the basket. kg

Perfect! Total weight of fruits = 22.25 kg.

(2) Subtract 7.425 from 12.85.

Excellent! Line up decimal places carefully.

(3) Multiply 1.25 by 0.48.

Correct! 2 + 2 = 4 decimal places in the product.

(4) Divide 78 by 2116.

Perfect! Simplify by dividing by 56.

(5) A car travels 45.6 km in the morning and 38.75 km in the evening. Find the total distance travelled. km

Excellent! Total distance travelled = 84.35 km.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) 0.125 × 0.8 =

(a) 0.1 (b) 0.08 (c) 0.01 (d) 1.0

0.1

0.08

0.01

1.0

Correct! 0.125 × 0.8 = 0.1.

(2) The reciprocal of 79 is:

(a) 97 (b) 79 (c) 1 (d) −97

9/7

7/9

-9/7

Correct! Reciprocal means flip the fraction: 79 becomes 97.

(3) 8.4 − 6.375 =

(a) 2.025 (b) 2.125 (c) 2.015 (d) 2.035

2.025

2.125

2.015

2.035

Correct! 8.400 − 6.375 = 2.025.

(4) 3 12 as an improper fraction is:

(a) 62 (b) 72 (c) 52 (d) 92

6/2

7/2

5/2

9/2

Correct! 3 12 = 3×2+12 = 72.

(5) 0.9 ÷ 0.3 =

(a) 3 (b) 0.3 (c) 0.09 (d) 30

0.3

0.09

Correct! 0.9 ÷ 0.3 = 9 ÷ 3 = 3.

(6) 1425 × 57 =

(a) 25 (b) 514 (c) 1 (d) 52

2/5

5/14

5/2

Correct! 1425 × 57 = 70175 = 25.

(7) 5.25 + 4.125 =

(a) 9.375 (b) 9.25 (c) 9.425 (d) 9.5

9.375

9.25

9.425

9.5

Correct! 5.25 + 4.125 = 9.375.

(8) Which is greater: 0.67 or 23?

(a) 0.67 (b) 23 (c) Equal (d) Cannot say

0.67

2/3

Equal

Cannot say

Correct! 0.67 > 23 (since 2/3 = 0.666...).

(9) 815 ÷ 1645 =

(a) 32 (b) 23 (c) 56 (d) 65

3/2

2/3

5/6

6/5

Correct! 815 ÷ 1645 = 815 × 4516 = 360240 = 32.

(10) 12.48 − 7.25 =

(a) 5.23 (b) 5.13 (c) 5.25 (d) 5.28

5.23

5.13

5.25

5.28

Correct! 12.48 − 7.25 = 5.23.

8/15 ÷ 16/45

7/12 + 5/18

7/8 ÷ 21/16

19/20 − 13/15

14/25 × 5/7

1.25 × 0.48

5/6 × 9/10

8.4 − 6.375

Fraction Add/Subtract

Fraction Multiplication

Fraction Division

Complex Decimals

Complex Fraction and Decimal Operations True or False

Determine whether these statements are True or False:

0.375 = 3/8

7/12 + 5/18 = 12/30

7/8 ÷ 21/16 = 2/3

0.125 × 0.8 = 0.01

0.67 > 2/3

4 3/5 = 23/5

Fractions and Decimals - Hard Quiz

🎉 Outstanding Mastery! Advanced Fraction and Decimal Excellence Achieved:

You have successfully conquered the "Fractions and Decimals (Hard)" worksheet and mastered:

(1) Complex Decimal Conversions: Converting challenging decimals like 0.375 and 0.125 to exact fraction forms

(2) Advanced Fraction Addition: Adding fractions with different denominators requiring complex LCD calculations

(3) Sophisticated Fraction Subtraction: Subtracting fractions across different denominators with multi-step simplification

(4) Fraction Multiplication Mastery: Multiplying fractions and reducing to simplest form efficiently

(5) Fraction Division Expertise: Dividing fractions using the multiply-by-reciprocal method

(6) Multi-place Decimal Operations: Working confidently with decimals to three and four decimal places

(7) Advanced Mixed Number Operations: Converting between mixed numbers and improper fractions fluently

(8) Complex Word Problem Solving: Applying operations to real-world scenarios with multiple steps

(9) Precision in Decimal Calculations: Maintaining accuracy in complex decimal multiplication and division

(10) Advanced Comparison Skills: Comparing fractions and decimals across different forms (0.67 vs 2/3)

(11) Reciprocal Applications: Understanding and applying reciprocal concepts in division problems

(12) Multi-step Simplification: Reducing complex fraction results to simplest form

(13) Advanced LCD Techniques: Finding least common denominators for challenging fraction pairs

(14) Decimal Place Value Mastery: Understanding and working with thousandths and ten-thousandths

(15) Strategic Problem-Solving: Choosing optimal methods for complex fraction and decimal operations

(16) Computational Accuracy: Maintaining precision across multi-step calculations

(17) Real-world Applications: Solving sophisticated practical problems involving measurements and quantities

(18) Mathematical Communication: Expressing complex fraction and decimal relationships clearly

Exceptional achievement! You've mastered advanced fraction and decimal operations with mathematical sophistication!

Sign in to Innings2

Fractions and Decimals

Reset Progress

Glossary