math 5

1. MTAP Program of
Excellence in Mathematics
Grade 5 Session 5
Name of Facilitator

2. RATIO

3. A. Rewrite the following fractions into ratio
(a:b).
𝟏
𝟐
𝟐
𝟑
𝟏𝟒
𝟏𝟕
1.
2.
3.
4. 𝟓
𝟒𝟗
5. 𝟐𝟓
𝟓𝟏
𝟏𝟐𝟏
𝟏𝟓𝟎
6.
7.𝟏𝟒𝟕
𝟐𝟓𝟑
8.𝟕𝟎𝟒
𝟓𝟐𝟓
9.
𝒙
𝒚
10. 𝟑𝒂
𝟓𝒃
= 1:2
= 2:3
= 14:17
= 5:49
= 25:51
= 121:150
= 147:253
= 704:525
= x:y
= 3a:5b

4. B. Find the ratio of each of the following.
1. 7 red ballpens to 11 green ball pens 7:11
2. 35 male student to 37 female students 35:37
3. 27 math books to 39 science books 27:39
4. 20 pesos to 50 pesos 20:50
5. 35 rams per 100 gram 35:100

5. B. Find the ratio of each of the following.
6. 5 teachers to 47 students 5:47
7. 17 boy scouts to 30 girl scouts 17:30
8. 4 mistakes out of 15 item quiz 4:15
9. 39 minutes is to 60 minutes 39:60
10. The ratio of 16 pencils to 25 papers 16:25

6. C. Simplify each ratio.
1. 5:15 =
2. 18:9 =
3. 42:63 =
4. 14:196 =
5. 34:127 =
1: 5
2:1
2:3
1:14
34:127
6. 130: 26 =
7. 150: 300 =
8. 250: 150 =
9. 6 206: 9 309 =
10. ¾ : 3/8 =
5: 1
1:2
5:3
2:3
÷ 5
÷9
÷ 21
÷14
÷ 26
÷ 150
÷ 25
÷3103
÷ 3/8
2:1

7. RATIO AND PROPORTION
.

8. D. Tell which of the following forms a proportion.
Write P if is a Proportion otherwise write NP.
1.
1
3
=
4
12
2. 8:4 = 12:15
3. 5: 20 = 1: 4
4. 17: 51 = 1: 3
5.
6
12
=
5
10
P
NP
P
P
P
6. 16: 19 = 5 : 6
7.
102
4
=
3
5
8. 8: 9 = 24: 27
9.
21
50
=
17
60
10.
1.5
4.5
=
1.8
5.76
NP
NP
NP
P
NP

9. E. Solve the missing number.
𝒏
𝟏𝟎
=
𝟑
𝟓
1.
2.
3.
4.
5.
→ 5n = 30
𝟑
𝒏
=
𝟗
𝟐𝟏
𝒏
𝟏𝟎
=
𝟐𝟏
𝟏𝟓
𝟒
𝒏
=
𝒏
𝟗
𝟏𝟔
𝟔𝟒
=
𝒏
𝟖𝟖
→ n = 6
→ 9n = 63 → n = 7
→ 15n = 210 → n = 14
→ n2 = 36 → n = 6
→ 𝟔𝟒n = 1408 → n = 22

10. E. Solve the missing number.
8: ___ = 12: 15
6.
7.
8.
9.
10.
4:6 = ___ : 12
___:10 = 2:5
4: ____ = ___ : 25
36 : ___ = 6:7
→ 12n = 120 → n = 10
→ 6n = 48 → n = 8
→ 5n = 20 → n = 4
→ n2 = 100 → n = 10
→ 6n = 252 → n = 42
10
8
4
10 10
42

11. FRACTION, DECIMAL AND PERCENT
.

12. F. Study the given table and fill in the empty spaces.
FRACTION DECIMAL PERCENT
1. 3/5
2. 0.28
3. 40%
4. 0.5
5. 88%
0.6 60 %
7/25 28 %
2/5 0.4
50 %
1/2
22/25 0.88

13. G. Change the following numbers to percent and vice
versa.
1. 0.15 =
2. 0.075 =
3. 0.06 =
4. 0.123 =
5. 0.99 =
15 %
7.5 %
6 %
12.3 %
99 %
6. 3 % =
7. 51 % =
8. 4 % =
9. 35 % =
10 2 % =
0.03
0.51
0.04
0.35
0.02

14. SOLVING WORD
PROBLEMS

15. H. Answer each of the following problems:
1. Given the number 14, 42, and 54. Answer the following questions.
a. What is the ratio of 14 to 42? _____________
b. Find the ratio of 14 to 54. ________________
c. What is the ratio of 42 to 54? _____________
Answer:
a. 14:42 = 1:3 or 1/3
b. 14:54 = 2:3 or 2/3
c. 42:54 = 7:9 or 7/9

16. 2. The ratio of boys to girls in a classroom is 5:7. If there are 84 students, how
many are boys?
Answer:
5n + 7n = 84, 12n = 84, n= 7, therefore, 5(n) = 5(7) = 35.
There are 35 boys in the classroom.

17. 3. In a farm, the ratio of a goat to duck is 4:14. If there are 24 goats, how many
are ducks?
Answer:
The ratio of goats to ducks is 4:14, if there are 24 goats then 4:14 =
24: n, 4n = 336, n=84. Then, there are 84 ducks.

18. 4. Two numbers are in the ratio 3:4 and the smaller number is 78. How much is
the larger number?
Answer:
¾ = 78/n, then 3n= 312, n = 104. Therefore, the larger number is
104.

19. 5. In a bookshelf, the ratio of fiction books to non-fiction is 19:11. If there are 57
fiction books, how many are non-fiction?
Answer:
19:11 = 57/n, 19n = 627,n = 33. Therefore, there are 33 non-fiction
books in a bookshelf

20. 6. Study the 10 x 10 square divided into 100 smaller squares
in which some have been shaded to form some shaded regions.
Give the number of shaded squares in each region as a
percent of all the small squares in the big square.
a. A = ________ b. B = ________
Answer:
A – 24 squares are shaded; A = 24/100 of the big square, so A is
24% of the big square; B is 35 % of it.

21. 7. The graph shows the preferred softdrinks in a school. Let us call the best
preferred softdrinks as A, B, C and D needed the rest as Other Brands or E. Out
of 100 bottles sold, the fraction of all softdrinks that brand represent is given.
Give the actual number per 100 bottles sold.
A._________ B._________ C._________
D._________ E. Other Bands _________
A – 30 bottles B - 20 bottles C - 18 bottles
D -17 bottles E - 15 bottles
Answer:

22. 8. Four workers can finish 12 chairs in 7 days. How many chairs can be finished
by 10 workers in 14 days working at the same rate?
Answer:
Suppose 4 workers can finish 12 chairs in 7 days. Then,
8 workers can finish 24 chairs in 7 days and 2 workers can finish
6 chairs in 7 days. So, 10 workers can finish 60 chairs in 14 days

23. 9. Edrian picked 90 mangoes. If 54 are not ripe, what percent of the mangoes
are ripe?
If 54 out of 90 mangoes are not ripe, then 90 – 54 = 36 are ripe.
36/90 = 2/5. Thus, 40 % are ripe.
Answer:

24. 10. A pair of slippers is sold at a 20& discount, If the original price of the slippers
is Php 550.
a. How much is the discount? __________
b. What is the discounted price? __________
a. 20% = 0.20 x 550 = 110. Therefore, the discount is 110.00
b. 550 – 110 = 440. Therefore, the discounted price is 440.00
Answer:

25. CHALLENGE!

26. Let us apply what we
learned!

27. Solve the following problems.
1. Mother divided 370.00 to her three sons for their baon. The
second child got ¼ of the third child’s part. And the ratio
between the first and the third son is 3:5. Find the money of
each son.
Let the ratio of the 1st and 3rd be 3x:5x, the second is ¼(5x) = 5x/4. So,
3x+(5x/4)+5x = 370, then 12x+5x+20x = 370, so (37x/4) = 370, 37x =1480,
so x = 40: First son = 3x= 3(40)=120.00; Second Son= 5x/4 = 5(40)/4 =
5(10)=50.00 and the third son is 5x=5(40)=200.00.

28. 2. The ratio of John’s money to Gavin was 4:7 at first. After
John spent ½ of his money and Gavin spent 360.Gavin had
twice as much money as John. How much money did John
have at first?
At first the ratio is 4:7, then after they spent some of the money
it became , 4n:7n-360, and Gavin had 7n-360 = 2(4n/2), 7N-360 = 4n, n=
120, since John has 4n, therefore he had 4(120) = 480. Therefore, John
had 480.00 at first

29. 3. I am a two digit number less than 100. I am a product of two
prime numbers. The sum of my digits is a 1-digit prime and one of
my digits is a prime. If you reverse my digits, I am prime. What
number am I?
Consider 34 which less than 100. It is the product of two prime
numbers, 2 x 17 = 34. The sum of the digits, 4 + 3 = 7 which is prime.
Reversing the digits gives 43 which is prime. Finally, one of its digits,
3 is a one-digit prime. So, 34 satisfy all conditions of the problem.

30. 4. There are 2960 students in a school. Of these, 20% walk to
school, 60% come to school by public transportation, 15% come
by school bus and the rest by private cars. How many students
come to school by each method?
Of the 2960 students in a school, 20% (.0.2 x 2960) = 592 walk
to school; 60% (0.6 x 1850) = 1,776 come to school by public
transportation; 20% (0.15 x 2960) = 444 come by school bus and the
rest, 2960 – (592 + 1,776 + 444) = 148 come to school by private cars.

31. 5. In a floor design made from tiles each of dimensions 40cm by 50cm,
find the ratios of:
(a) The perimeter of unshaded portion to the perimeter of the whole
design.
(b) The area of the shaded portion to the area of the unshaded portion.
a. Sol’n: PWHOLE = 2L + 2W PSHADED = 2L + 2W PUNSHADED = 180-100
= 2(40) + 2(50) =2(20) +2(30) = 80 cm
= 80 + 100 = 40 + 60
= 180 cm = 100 cm
Therefore, PUNSHADED:PWHOLE = 80:180 = 4:9

32. 5. In a floor design made from tiles each of dimensions 40cm by 50cm,
find the ratios of:
(a) The perimeter of unshaded portion to the perimeter of the whole
design.
(b) The area of the shaded portion to the area of the unshaded portion.
b. Sol’n: AWHOLE = LW ASHADED = LW AUNSHADED = 2000-600 cm2
= 40(50) =20(30) = 1400 cm2
= 2000 cm2 =600 cm2
Therefore, ASHADED:AUNSHADED = 600:2000 = 3:7