Maths Questions With Answers on Ratios for Grade 5

Questions on how to find maths ratios in different situations are presented along with detailed step-by-step solutions and explanations.

Questions and Step-by-Step Solutions

  1. Question 1: In the figure below are three different shapes: squares, triangles, and circles.

    ratios, question 1

    Use the above picture to find the following ratios:

    1. the ratio of the number of triangles to the number of circles
    2. the ratio of the number of circles to the number of squares
    3. the ratio of the number of triangles to total number of shapes
    4. the ratio of the number of circles to total number of shapes
    5. the ratio of the number of circles to number of triangles
    ► View Step-by-Step Solution

    Based on the image counts, there are 9 triangles, 6 circles, and 3 squares (Total = 18 shapes).

    A) Triangles to circles = 9 to 6

    B) Circles to squares = 6 to 3

    C) Triangles to total shapes = 9 to 18

    D) Circles to total shapes = 6 to 18

    E) Circles to triangles = 6 to 9

  2. Question 2: There are 15 apples, 10 bananas, and 5 pears in a basket. Use the given information to find the following ratios:

    1. the ratio of the number of bananas to the total number of fruits
    2. the ratio of the number of pears to the number of apples
    3. the ratio of the number of bananas to the number of apples
    4. the ratio of the number of pears to the total number of fruits
    5. the ratio of the number of apples to the total number of fruits
    ► View Step-by-Step Solution

    Total fruits = 15 (apples) + 10 (bananas) + 5 (pears) = 30 fruits.

    A) Bananas to total fruits = 10 to 30

    B) Pears to apples = 5 to 15

    C) Bananas to apples = 10 to 15

    D) Pears to total fruits = 5 to 30

    E) Apples to total fruits = 15 to 30

  3. Question 3: In a school, there are 120 boys and 180 girls. 40 of the boys are under 10 years and 140 of the girls are under 10 years. Use the given information to find:

    1. the ratio of the number of boys to the number of girls
    2. the ratio of the number of boys who are less than 10 to the number of boys who are 10 or older (in simplest form)
    3. the ratio of the number of girls who are less than 10 to the number of boys who are 10 or older (in simplest form)
    4. the ratio of the number of girls who are 10 or older to the total number of pupils (in simplest form)
    5. the ratio of the number of girls who are less than 10 to the total number of pupils who are 10 or older (in simplest form)
    ► View Step-by-Step Solution

    Given Data:
    - Total boys = 120 (40 under 10, so \(120 - 40 = 80\) boys are 10 or older)
    - Total girls = 180 (140 under 10, so \(180 - 140 = 40\) girls are 10 or older)
    - Total pupils = \(120 + 180 = 300\)

    A) Boys to girls = \(120 : 180 = 2 : 3\) (or 2 to 3)

    B) Boys < 10 to boys \(\ge\) 10 = \(40 : 80 = 1 : 2\) (or 1 to 2)

    C) Girls < 10 to boys \(\ge\) 10 = \(140 : 80 = 7 : 4\) (or 7 to 4)

    D) Girls \(\ge\) 10 to total pupils = \(40 : 300 = 2 : 15\) (or 2 to 15)

    E) Girls < 10 to total pupils \(\ge\) 10 (boys \(\ge\) 10 [80] + girls \(\ge\) 10 [40] = 120) = \(140 : 120 = 7 : 6\) (or 7 to 6)

  4. Question 4: Let \(a\), \(b\), and \(c\) be the number of blue, yellow, and white marbles in a box, respectively. Given that \(a > b\) and \(b > c\), answer True or False to the following statements:

    1. The ratio of blue marbles to the total number of marbles is less than the ratio of white marbles to the total number of marbles.
    2. The ratio of yellow marbles to the total number of marbles is greater than the ratio of blue marbles to the total number of marbles.
    3. The ratio of white marbles to the total number of marbles is less than the ratio of blue marbles to the total number of marbles.
    ► View Step-by-Step Solution

    Total marbles = \(a + b + c\).

    A) Ratio of blue to total is \(\dfrac{a}{a+b+c}\), and white to total is \(\dfrac{c}{a+b+c}\). Since \(a > c\), \(\dfrac{a}{a+b+c} > \dfrac{c}{a+b+c}\). Thus, the statement is False (F).

    B) Ratio of yellow to total is \(\dfrac{b}{a+b+c}\), and blue to total is \(\dfrac{a}{a+b+c}\). Since \(b < a\), \(\dfrac{b}{a+b+c} < \dfrac{a}{a+b+c}\). Thus, the statement is False (F).

    C) Ratio of white to total is \(\dfrac{c}{a+b+c}\), and blue to total is \(\dfrac{a}{a+b+c}\). Since \(c < a\), \(\dfrac{c}{a+b+c} < \dfrac{a}{a+b+c}\). Thus, the statement is True (T).

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