MYP 3 · Maths
REAL NUMBERS AND RATIO
Operations with decimal numbers
QUESTION 1 [6 marks] — Criterion B
Medium
Investigate what happens when you square a decimal number between 0 and 1.
a.
Calculate $(0.9)^2$, $(0.5)^2$, and $(0.3)^2$.
[2] Show Solution
$(0.9)^2=0.81$. $(0.5)^2=0.25$. $(0.3)^2=0.09$.
b.
In each case, compare the squared result to the original number. What do you notice?
[2] Show Solution
In every case, the squared result is smaller than the original number (e.g. $0.81<0.9$, $0.25<0.5$, $0.09<0.3$).
c.
Explain why this happens, using the idea of multiplying a number by 'a fraction of itself'.
[2] Show Solution
Squaring a number less than 1 means multiplying it by another number less than 1, which is the same as finding a fraction of the original number — and a fraction of something is always less than the whole thing (for positive numbers), so the result is always smaller than the original.
QUESTION 2 [6 marks] — Criterion C
Medium
Calculate $$4.8 - 2.35 \times 1.6 \div 0.4$$
a.
Show every step of your working, clearly stating which operation is performed at each stage, and give your final answer correct to 2 decimal places.
[4] Show Solution
Multiplication/division first (left to right): $2.35\times1.6=3.76$, then $3.76\div0.4=9.4$. Then subtraction: $4.8-9.4=-4.6$. Final answer: $-4.60$.
b.
A classmate got a different answer by calculating $4.8-2.35$ first. Explain what error they made.
[2] Show Solution
They performed the subtraction before the multiplication and division, which violates the order-of-operations convention — multiplication and division must be carried out before subtraction unless brackets say otherwise.
QUESTION 3 [5 marks] — Criterion D
Medium
A phone plan costs \$45.90 per month, plus \$0.35 per minute for calls beyond the included minutes, plus \$0.12 per SMS beyond the included texts.
a.
In one month, a customer used 40 extra minutes and sent 25 extra texts. Calculate their total bill for the month.
[3] Show Solution
Extra minutes cost: $40\times0.35=14.00$. Extra texts cost: $25\times0.12=3.00$. Total: $45.90+14.00+3.00=62.90$.
b.
The customer budgeted \$60 for their phone bill this month. By how much have they gone over budget, and suggest one way they could reduce next month's bill.
[2] Show Solution
They went over budget by $62.90-60.00=\$2.90$. They could reduce next month's bill by making fewer extra calls or sending fewer extra texts (e.g. using a messaging app over Wi-Fi instead of SMS).