5. Fractions

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Fractions – Full Notes + Stepwise Solutions (Problem Sets 17–23)

Fractions – Notes & Step-by-Step Solutions Problem Sets 17–23

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1) Concept Notes (Definitions, Rules & Examples) 2) Problem Set 17 – Equivalent Fractions 3) Problem Set 18 – Convert to Like Fractions 4) Problem Set 19 – Compare Fractions (<, >, =) 5) Problem Set 20 – Addition (Same Denominators) + Word Problems 6) Problem Set 21 – Subtraction (Same Denominators) + Word Problem 7) Problem Set 22 – Addition & Subtraction (Different Denominators) 8) Problem Set 23 – “Fraction of a Collection / Number”

1) Concept Notes

What is a fraction? A number written as numeratordenominator. The denominator tells the number of equal parts; the numerator tells how many parts are taken.
Equivalent Fractions represent the same value. Multiply or divide the numerator and the denominator by the same non-zero number. Example: 23 = 2×43×4 = 812.
Like Fractions have the same denominator (e.g., 38 and 58). To convert unlike fractions to like fractions, change them to a common denominator (usually the LCM).
Adding/Subtracting Fractions • If denominators are the same: add/subtract only the numerators. • If denominators differ: convert to like fractions first. Example: 16 + 14 = 212 + 312 = 512.
Compare Fractions • Same denominator → compare numerators. • Same numerator → the fraction with the smaller denominator is larger. • Otherwise, convert to like fractions or cross-multiply.
Fraction “of” a number means multiplication. Example: 35 of 20 = 35 × 20 = 12.
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2) Problem Set 17 – Equivalent Fractions

1) Write the proper number in the box.
  1. 12 = □20
    Denominator doubled by ×10, so numerator also ×10 → 1×102×10 = 1020. Answer: 10.
  2. 34 = 15□
    3 → 15 is ×5, so 4 → 4×5 = 20. Answer: 20.
  3. 911 = 18□
    9 → 18 is ×2; 11×2 = 22. Answer: 22.
  4. 1040 = □8
    Simplify 10/40 = 1/4. Make denominator 8 (×2) → 2/8. Answer: 2.
  5. 1426 = □13
    Divide both by 2 → 7/13. Answer: 7.
  6. □3 = 46
    4/6 simplifies to 2/3. So numerator is 2.
  7. 1□ = 420
    4/20 = 1/5 ⇒ denominator is 5.
  8. □5 = 1025
    10/25 = 2/5 ⇒ numerator is 2.
2) Find an equivalent fraction with denominator 18.
GivenTo denominator 18Working
12918×9
231218×6
461218×3
29418×2
791418×2
533018×6
3) Find an equivalent fraction with denominator 5.
GivenEquivalent with denom 5Working
61525÷3
102525÷5
123025÷6
61035÷2
213535÷7
4) Pair off the equivalent fractions.
Given: 2/3, 5/7, 5/11, 7/9, 14/18, 15/33, 18/27, 10/14. Pairs → 2/3 ↔ 18/27 (÷9), 5/7 ↔ 10/14 (×2), 5/11 ↔ 15/33 (×3), 7/9 ↔ 14/18 (×2).
5) Two equivalent fractions for each:
GivenTwo equivalents
791418, 2127
45810, 1215
311622, 933
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3) Problem Set 18 – Convert into Like Fractions

Find the LCM of the denominators and rewrite each pair with that denominator.

#GivenLCMLike FractionsSteps
13/4 , 5/886/8 , 5/83/4 = 6/8
23/5 , 3/73521/35 , 15/35×7 and ×5
34/5 , 3/10108/10 , 3/104/5 = 8/10
42/9 , 1/6184/18 , 3/18×2 and ×3
51/4 , 2/3123/12 , 8/12×3 and ×4
65/6 , 4/53025/30 , 24/30×5 and ×6
73/8 , 1/6249/24 , 4/24×3 and ×4
81/6 , 4/9183/18 , 8/18×3 and ×2
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4) Problem Set 19 – Write <, > or =

#ComparisonAnswerReason
13/7 ? 3/7=Same fraction.
23/8 ? 2/8>Same denom; 3>2.
32/11 ? 10/11<Same denom; 2<10.
45/15 ? 10/30=Both = 1/3.
55/8 ? 5/9>Same numerator; smaller denom ⇒ larger value.
64/7 ? 4/11>Same numerator; 7<11 ⇒ 4/7 larger.
710/11 ? 10/13>Same numerator; 11<13 ⇒ 10/11 larger.
81/5 ? 1/9>Same numerator; 5<9 ⇒ 1/5 larger.
95/6 ? 1/8>0.833… vs 0.125
105/12 ? 1/6>5/12 vs 2/12
117/8 ? 14/16=14/16 reduces to 7/8
124/9 ? 4/9=Same fraction
135/18 ? 1/9>1/9 = 2/18; 5/18 > 2/18
142/3 ? 4/7>Cross-multiply: 2×7=14 > 3×4=12
153/7 ? 5/9<3×9=27 < 7×5=35
164/11 ? 1/5>4×5=20 > 11×1=11
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5) Problem Set 20 – Addition (Same Denominators) + Word Problems

1) Add:
  1. 15 + 35 = 45
  2. 27 + 47 = 67
  3. 712 + 212 = 912 = 34
  4. 29 + 79 = 99 = 1
  5. 315 + 415 = 715
  6. 27 + 17 + 37 = 67
  7. 210 + 410 + 310 = 910
  8. 49 + 19 = 59
  9. 58 + 38 = 88 = 1
2) Word Problem
Meena gets 38 of a guava, Geeta gets 28. Total = 3/8 + 2/8 = 58 of a guava.
3) Word Problem
Girls cleaned 34 of the field; boys cleaned 14. Total = 3/4 + 1/4 = 4/4 = 1 whole field.
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6) Problem Set 21 – Subtraction (Same Denominators) + Word Problem

1) Subtract:
  1. 5/7 − 1/7 = 47
  2. 5/8 − 3/8 = 2/8 = 14
  3. 7/9 − 2/9 = 59
  4. 8/11 − 5/11 = 311
  5. 9/13 − 4/13 = 513
  6. 7/10 − 3/10 = 4/10 = 25
  7. 9/12 − 2/12 = 712
  8. 10/15 − 3/15 = 715
2) Word Problem
To be painted = 7/10; already painted = 4/10. Left = 7/10 − 4/10 = 310 of the wall.
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7) Problem Set 22 – Addition & Subtraction (Different Denominators)

1) Add:
  1. 1/8 + 3/4 = 1/8 + 6/8 = 78
  2. 2/21 + 3/7 = 2/21 + 9/21 = 1121
  3. 2/5 + 1/3 = 6/15 + 5/15 = 1115
  4. 2/7 + 1/2 = 4/14 + 7/14 = 1114
  5. 3/9 + 3/5 = 1/3 + 3/5 = 5/15 + 9/15 = 1415
2) Subtract:
  1. 3/10 − 1/20 = 6/20 − 1/20 = 14
  2. 3/4 − 1/2 = 3/4 − 2/4 = 14
  3. 6/14 − 2/7 = 6/14 − 4/14 = 17
  4. 4/6 − 3/5 = 2/3 − 3/5 = 10/15 − 9/15 = 115
  5. 2/7 − 1/4 = 8/28 − 7/28 = 128
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8) Problem Set 23 – Fraction of a Collection / Number

1) What is 13 of each collection?
CollectionWorkingAnswer
15 pencils15 ÷ 35 pencils
21 balloons21 ÷ 37 balloons
9 children9 ÷ 33 children
18 books18 ÷ 36 books
2) What is 15 of each?
QuantityWorkingAnswer
20 rupees20 ÷ 54 rupees
30 km30 ÷ 56 km
15 litres15 ÷ 53 litres
25 cm25 ÷ 55 cm
3) Find the part equal to the given fraction.
ExpressionWorkingAnswer
23 of 3030 ÷ 3 = 10; 10 × 220
711 of 2222 ÷ 11 = 2; 2 × 714
38 of 6464 ÷ 8 = 8; 8 × 324
513 of 6565 ÷ 13 = 5; 5 × 525
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— End of Notes & Solutions —

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