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Practice: ratio and scale

Practice: ratio and scale

1

Write as a reduced ratio.

a

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

    b

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

      c

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

        d

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

          2

          A class has 12 boys and 16 girls.
          Write as a reduced ratio:

          • the ratio of boys to girls;
          • the ratio of girls to all the students;
          • the ratio of boys to all the students.
          3

          Fill in the missing number, so that the ratios are equal.

          3:5=12:□\displaystyle {3:5}={12:\square} \displaystyle \quad 7:2=□:10\displaystyle {7:2}={\square:10} \displaystyle \quad 4:9=20:□\displaystyle {4:9}={20:\square} \displaystyle \quad 15:25=□:5\displaystyle {15:25}={\square:5}

          3:5=12:□\displaystyle {3:5}={12:\square}

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

            7:2=□:10\displaystyle {7:2}={\square:10}

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

              4:9=20:□\displaystyle {4:9}={20:\square}

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                15:25=□:5\displaystyle {15:25}={\square:5}

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                  / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                  4

                  Raspberry juice has 2 cups of syrup for every 7 cups of water.
                  Roni wants to make juice that tastes the same from 21 cups of water.
                  How many cups of syrup does he need?

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                    / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                    5

                    Two friends bought a ball together for 60 ₪.
                    They paid in the ratio 5:7\displaystyle 5:7.
                    How much did each of them pay?
                    Draw a strip of the ratio, too.

                    The first friend

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                      / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                      The second friend

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                        / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                        6

                        On a map, 3 cm stand for 6 km in reality.
                        6 km are 600,000\displaystyle 600{,}000 cm.
                        Write the map’s scale so that one of its numbers is 1.

                          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                          / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                          7

                          On a map at a scale of 1:200,000\displaystyle 1:200{,}000 the road between two towns is 7.5 cm long.
                          How long is the road in reality, in kilometres?

                            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                            / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power

                            8

                            A rectangular garden is drawn on a plan at a scale of 1:100\displaystyle 1:100, 3 cm long and 2 cm wide.
                            Noa says: “The garden’s area on the plan is 6 cm², so in reality it is 600 cm².”
                            Is she right?
                            Explain, and find the real garden’s area in m².

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power

                              / – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power