Unit 1 test: Algebra

What is $98 \times 102 - 99 \times 101$?

What is $\dfrac{1}{2 \cdot 3} + \dfrac{1}{3 \cdot 4} + \dfrac{1}{4 \cdot 5} + \dots + \dfrac{1}{9 \cdot 10}$? Express your answer as a common fraction.

The price of a bike is raised by $20\%$. Later the new price is lowered by $25\%$. Compared with the original price, the final price is

Write $0.\overline{45}$ as a common fraction in lowest terms.

The ratio of boys to girls in a grade is $5 : 7$. There are $96$ students in the grade. How many are girls?

If $a : b = 3 : 4$ and $b : c = 2 : 5$, what is $a : c$?

The sum of four consecutive odd integers is $136$. What is the smallest of them?

A pet store has only birds and rabbits. Altogether there are $25$ heads and $70$ legs. How many rabbits are there?

Two runners are $10$ kilometers apart on a straight road and run toward each other, one at $6$ km/h and the other at $9$ km/h. How many minutes pass before they meet?

Alex can mow a lawn in $3$ hours. Working together, Alex and Blake can mow it in $2$ hours. How many hours would Blake take alone?

How many multiples of $7$ are between $100$ and $500$?

The digits $1, 2, 3, 3, 2, 1$ repeat forever: $123321123321\dots$ What is the sum of the first $2026$ digits?

The average of six numbers is $20$. The average of the first four is $17$. What is the average of the last two?

A team of $10$ players has an average weight of $150$ pounds. When one player leaves and a new player joins, the average weight becomes $153$ pounds. The new player weighs $175$ pounds. How much did the player who left weigh, in pounds?