Learning guides
Understand readings and expressions, then put them into practice with review and mock tests.
数値 and 数字: measured values and numerical notation
Compare 数値 for a numerical value with 数字 for digits or contextual figures, including sales figures that are not identification numbers.
桁 and 桁違い: digit positions and a striking difference
Distinguish a digit-position error in an amount from a striking difference in a record, without assigning a fixed multiplier to 桁違い.
整数: a number format that includes negative integers
Read instructions to express an answer as an integer separately from counting objects, including zero and negative integers.
約 and ぐらい: approximation before and after a quantity
Compare the placement of 約百人 and 五キロぐらい, keeping a number together with its counter or unit.
概算 and 計算: an estimated cost and the act of calculation
Compare roughly estimating material costs with carrying out a calculation, without treating calculation alone as proof of an accurate final amount.
数十 and 多数: a scale of several tens and a large number
Compare the scale expressed by 数十人 with the assessment 多数, without inventing an exact participant or exhibit count.
複数 and 多数: more than one and an assessment of many
Separate the condition of more than one in 複数 from the assessment of many in 多数, without inferring a large number or a majority from plurality.
一杯: one cup and a state of being full
Compare the structures お茶を一杯 and 人で一杯 without treating one drink as a specified volume or proof of a full container.
等分 and 均等: equal parts and an even distribution
Compare dividing a cord into four equal parts with force distributed evenly, keeping the part count separate from each part’s size.
中央値 and 平均: the middle ordered value and the arithmetic mean
Find the median of an odd number of ordered values and compare it with adding all values and dividing to obtain an arithmetic mean.
倍 and 倍数: a size relationship and a multiple condition
Compare a twofold relationship between quantities with the condition of being a multiple, then select qualifying numbers.
差 and 比率: subtraction and a relative comparison
Read a difference separately from a ratio, using simple values to show that the same difference need not give the same ratio.
比例: a proportional relationship and a tendency to change
Read a stated proportional relationship such as circumference and diameter, without turning every ば〜ほど tendency into an exact mathematical proportion.
以上, 以下, and 未満: whether a quantity includes its boundary
Compare inclusive 以上 and 以下 with exclusive 未満 in weight and height conditions, then identify the scope of a prohibition.
換算 and 単位: different numbers for the same quantity
Convert lengths between meters and centimeters, distinguishing a numerical change from a quantity change and checking the conversion basis.
超過 and 過剰: exceeding a limit and exceeding what is needed
Compare exceeding a weight limit with excessive packaging, separating a numerical restriction from a purpose-based assessment.
上限, 下限, 最大, and 最小: prescribed limits and data extrema
Compare prescribed upper and lower limits with the maximum and minimum of an explicitly stated data set, checking where each figure comes from.
端数 and 切り捨て: a remainder in an amount and discarding it
Distinguish a remainder in an integer amount from a specified discarding rule, then check the amount before and after processing.
単価 and 総額: the price per unit and the purchase total
Connect the unit price with a stated purchase quantity, keeping one unit’s price separate from the total for the purchase scope.
差額 and 加算: a price difference and an added charge
Compare the difference between two prices with adding a charge to a base amount, keeping a separate amount distinct from the final amount.
実質: a smaller content amount at the same price
Read 実質的な値上げ when the posted price stays unchanged but less content is obtained for the same money.
残高, 収入, and 支出: a balance and incoming or outgoing money
Separate an account balance from incoming and outgoing amounts, reading a hypothetical balance change with no other changes.
収入 and 支出: read the same payment from each party’s view
Identify money moving in or out in hypothetical buyer and seller records for the same payment.
売上 and 利益: sales and profit after costs
Compare hypothetical sales with monetary profit after all stated costs, without transferring a large-sales assessment to profit.
赤字 and 黒字: a financial result and black lettering
Read deficit and surplus in a hypothetical income-and-expenditure record, then distinguish black lettering as another use of 黒字.
在庫 and 受注: goods in stock and an accepted production order
Separate current stock quantity from the quantity of an accepted order, without treating acceptance as finished goods already secured.
需要 and 供給: the quantity needed and the quantity provided
Separate demand for goods from the provision of materials, without turning a prepared quantity into completed sales.
定員 and 人数: a capacity limit and the actual count
Compare a course’s capacity with its stated participant count and read the condition behind closure when capacity is reached.
寸法 and 規格: drawing dimensions and conformity conditions
Compare a board’s actual dimension with its drawing, without extending agreement in one length to all specification requirements.
半径 and 直径: from the center and across a circle
Distinguish radius from diameter and identify which length a stated measurement describes.