Question

3 use numbers from the box to complete the equation
a. $0.8 \times 0.8 =$
b. $0.88 \times 1.1 =$
c. $8.8 \times 1.1 =$
d. $8.8 \times 0.1 =$
box: -0.088 0.6 -0.968 6.4

Explanation:

Part a

Step1: Multiply the decimals

To calculate \(0.8\times0.8\), we can think of it as \(8\times8 = 64\). Since both numbers have one decimal place, the product will have \(1 + 1=2\) decimal places. So we place the decimal point two places from the right in 64, giving \(0.64\). Wait, but looking at the box, maybe there was a typo or I misread. Wait, the box has 0.088, 0.6 (maybe 0.64? Maybe the box has 0.64 as 0.6? No, maybe the original problem's box has 0.64? Wait, no, the user's box shows -0.088, 0.6, -0.968, 6.4? Wait, maybe I misread. Wait, let's recalculate:

\(0.8\times0.8\): \(0.8\) is \(\frac{8}{10}\), so \(\frac{8}{10}\times\frac{8}{10}=\frac{64}{100} = 0.64\). But in the box, there's 0.6? Maybe a typo, but assuming the box has 0.64 as 0.6 (no, that's not right). Wait, maybe the user's box has 0.64, but it's written as 0.6? No, perhaps I made a mistake. Wait, no, let's check again.

Wait, maybe the box is: -0.088, 0.64, -0.968, 6.4? Maybe the user's image has 0.64 as 0.6? No, perhaps the original problem's box has 0.64, but let's proceed with the calculation.

Step1: Calculate \(0.8\times0.8\)

\(0.8\times0.8 = 0.64\) (if the box has 0.64, but in the given box, there's 0.6. Maybe a typo, but let's assume the correct answer is 0.64, but maybe the box has 0.6 as 0.64? No, perhaps I misread. Wait, the user's box: "-0.088 0.6 -0.968 6.4" – maybe 0.6 is 0.64? No, that's not. Wait, maybe the problem is different. Wait, no, let's do part b:

Part b

\(0.88\times1.1\): Let's calculate. \(0.88\times1.1\). We can write it as \(0.88\times(1 + 0.1)=0.88\times1+0.88\times0.1 = 0.88 + 0.088 = 0.968\). Ah! The box has -0.968, so that's the answer for part b.

Part c

\(8.8\times1.1\): \(8.8\times1.1\). Let's calculate: \(8.8\times1 = 8.8\), \(8.8\times0.1 = 0.88\), so total is \(8.8 + 0.88 = 9.68\)? Wait, no, \(8.8\times1.1 = 9.68\)? Wait, no, \(8\times1.1 = 8.8\), \(0.8\times1.1 = 0.88\), so \(8.8 + 0.88 = 9.68\)? But the box has 6.4? No, wait, \(8.8\times1.1\): \(8.8\times1.1 = (8 + 0.8)\times1.1 = 8\times1.1 + 0.8\times1.1 = 8.8 + 0.88 = 9.68\). But the box has -0.968, 6.4? Wait, no, maybe I made a mistake. Wait, \(8.8\times1.1\): \(8.8\times1.1 = 9.68\), but the box has 6.4? No, that's not. Wait, maybe the problem is \(8.8\times0.1\)? No, part d is \(8.8\times0.1\).

Part d

\(8.8\times0.1\): Multiplying by 0.1 moves the decimal one place left, so \(8.8\times0.1 = 0.88\). But the box has -0.088? No, \(8.8\times0.1 = 0.88\), but the box has -0.088. Wait, maybe the problem is \(0.88\times0.1\)? No, part d is \(8.8\times0.1\).

Wait, maybe there's a misprint in the box. Let's re-express each:

a. \(0.8\times0.8 = 0.64\) (if box has 0.64 as 0.6, but no)

b. \(0.88\times1.1\): Let's calculate \(0.88\times1.1\). \(0.88\times1 = 0.88\), \(0.88\times0.1 = 0.088\), so total is \(0.88 + 0.088 = 0.968\) (which is in the box: -0.968, maybe a typo with the negative, but the value is 0.968)

c. \(8.8\times1.1\): \(8.8\times1.1 = 9.68\)? But the box has 6.4? No, \(8.8\times1.1 = (8 + 0.8)\times1.1 = 8\times1.1 + 0.8\times1.1 = 8.8 + 0.88 = 9.68\). Wait, but the box has 6.4. Wait, maybe \(8.8\times0.8\)? No, the problem is \(8.8\times1.1\).

d. \(8.8\times0.1 = 0.88\), but the box has -0.088. Wait, \(0.88\times0.1 = 0.088\), which is in the box (with a negative sign, maybe a typo).

Ah! Maybe I mixed up the parts. Let's re-express:

a. \(0.8\times0.8 = 0.64\) (if box has 0.64 as 0.6, but no)

Wait, maybe the box is:

-0.088 (which is \(0.88\times0.1\)), 0.64 (which is \(0.8\times0.8\)), -0.968 (which is \(0.88\times1.1\) with a negative, may…

Step1: Multiply the decimals

\(0.8\times0.8\): Convert to fractions: \(\frac{8}{10}\times\frac{8}{10}=\frac{64}{100}=0.64\)

Step1: Distribute the multiplication

\(0.88\times1.1 = 0.88\times(1 + 0.1)=0.88\times1 + 0.88\times0.1 = 0.88 + 0.088 = 0.968\)

Answer:

\(0.64\) (if box has 0.64, else 0.6 as a typo)

Part b